Cómo reiniciar la aplicación Flutter programáticamente

import 'package:flutter/material.dart';

void main() {
  runApp(
    RestartWidget(
      child: MaterialApp(),
    ),
  );
}

class RestartWidget extends StatefulWidget {
  RestartWidget({this.child});

  final Widget child;

  static void restartApp(BuildContext context) {
    context.findAncestorStateOfType<_RestartWidgetState>().restartApp();
  }

  @override
  _RestartWidgetState createState() => _RestartWidgetState();
}

class _RestartWidgetState extends State<RestartWidget> {
  Key key = UniqueKey();

  void restartApp() {
    setState(() {
      key = UniqueKey();
    });
  }

  @override
  Widget build(BuildContext context) {
    return KeyedSubtree(
      key: key,
      child: widget.child,
    );
  }
}

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In this example you can reset your app from everywhere using RestartWidget.restartApp(context).
RakshaD